
import numpy as np

import matplotlib.pyplot as plt

from astropy.io import ascii
from astropy.table import Table

import scipy.stats as stats

import arviz as az
import stan

import nest_asyncio

import asteroids_functions as fast

import pickle


nest_asyncio.apply()


linelist = ascii.read("CC_CI1_Features.csv")


linelist


your_file = 'saponite_norm_T.txt'


spectrum = ascii.read(your_file)
spectrum['col1'] = spectrum['col1'] / 1000


spectrum


M = np.max(spectrum['col1'])      # set the size of the wavelength grid in micron
dM = np.diff(spectrum['col1'])[0] # the step in the wavelength grid
x = spectrum['col1']              # this is the wavelength grid
N = len(x)                        # the number of data points we have is related to the grid
ye = 0.01                         # error (noise)


fig, ax = plt.subplots(1, 1, figsize = (12, 5))

# plot the observed spectrum
ax.plot(x, spectrum['col4'], '-', lw = 2)
ax.legend(["Observed spectrum"])

# format
ax.set_xlabel(r"$\lambda$ (micron)")
ax.set_ylabel(r"Reflectance")
ax.set_ylim(0,1.1)

plt.tight_layout()

plt.show()


# specify the model for stan
stan_code = """ 
functions {
    real G(data real x, real phi, real mu, real sigma){
        return -phi * exp(-(x - mu)^2./(2.*sigma^2.));
    }
}

data {
    int<lower=0> K;                     // number of features (mixture components)
    int<lower=0> N;                     // number of data points (depends on how finely you sample the spectrum)
    vector[N] yo;                       // observations (literally the values of the reflectance at lambda)
    real ye;                            // error on observation
    vector[N] x;                        // wavelength grid
    real del;                           // size of the little box around each mean
    vector[K] mut;                      // means of the known features (sorted)
    vector[K] mut_l;                    // range of the known features (left bound)
    vector[K] mut_r;                    // ^^ (right bound)
}   
   
parameters {   

    // characteristics of the features (the gaussians we want to recover)
    
    real<lower = mut_l[1]-0.01, upper = mut_r[1]+0.01>  common_feats;    // locations of the features 
    real<lower = mut_l[2]-0.01, upper = mut_r[2]+0.01>   fe32_charge;
    real<lower = mut_l[3]-0.01, upper = mut_r[3]+0.01> fe2_crystal_1;
    real<lower = mut_l[4]-0.01, upper = mut_r[4]+0.01>     magnetite;
    real<lower = mut_l[5]-0.01, upper = mut_r[5]+0.01> fe2_crystal_2;
    real<lower = mut_l[6]-0.01, upper = mut_r[6]+0.01>   serpentines;
    real<lower = mut_l[7]-0.01, upper = mut_r[7]+0.01>  oh_saponites;
    real<lower = mut_l[8]-0.01, upper = mut_r[8]+0.01> h2o_saponites;
    real<lower = mut_l[9]-0.01, upper = mut_r[9]+0.01>        hoh_oh;
    
    vector<lower = 0>[K] sigma;                     // width of the feature
                                
    vector<lower = -0.01, upper = 1.5>[K] phi;      // (negative) depth of the feature
                                        
    real epsilon;                                   // continuum level (offset of the entire spectrum from 0 -- like an intercept)
    
}

transformed parameters{
    // the "line" of our linear regression
    vector[K] mus = [common_feats, fe32_charge, fe2_crystal_1, magnetite, fe2_crystal_2, serpentines, oh_saponites, h2o_saponites, hoh_oh]';
    vector[K] ps;                                   // placeholder
    vector[N] yt;                                   // noiseless "true" value, yo = phi*yt + epsilon
    
    // if phi of feature k is non-zero, it's contributing to the observed reflectance, so it's worth constraining its mean, SD
    // otherwise, it doesn't, but the model will still do its best to constrain them
    // so instead we don't include them in the likelihod, and their mean, SD become dependent on the initial guess    
    
    for (n in 1:N){
        for (k in 1:K){
            if (phi[k] > 0.01){
                ps[k] = G(x[n], phi[k], mus[k], sigma[k]);       // the features that are doing things
            }                                                    
            else{
                ps[k] = 0;                                       // the features that don't actually exist                                                           
            }
        }
        yt[n] = sum(ps) + epsilon;
    }

}

model{

    // priors
    
    phi ~ normal(0.5,0.5);                          // height of peak
       
    common_feats   ~ normal(mut[1], del);  // each mean is unique and ordered
    fe32_charge    ~ normal(mut[2], del);
    fe2_crystal_1  ~ normal(mut[3], del);
    magnetite      ~ normal(mut[4], del);
    fe2_crystal_2  ~ normal(mut[5], del);
    serpentines    ~ normal(mut[6], del);
    oh_saponites   ~ normal(mut[7], del);
    h2o_saponites  ~ normal(mut[8], del);
    hoh_oh         ~ normal(mut[9], del);
    
    epsilon ~ normal(1, 1);                         // continuum level

    sigma ~ normal(0.1, 0.05);                      // sigma
    
    
    // likelihood
    
    yo ~ normal(yt, ye);
}
"""


data = {}
data["K"] = 9                        # we have 9 features, although several of them should be 0 here
data["N"] = N                        # and N = M/dM samples on the curve
data["yo"] = spectrum['col4']        # and these are the values of the observed reflectance
data["ye"] = ye                      # with their error
data["x"] = x                        # at these values of lambda
data["del"] = 0.1                    # this is how big the little windowbox prior should be for each mu
data["mut"] = linelist['mean']       # and this is where we think they are
data["mut_l"] = linelist['left']     # ^^
data["mut_r"] = linelist['right']    # ^^


fit = stan.build(program_code = stan_code, data = data) # build the model

Building: found in cache, done.
Messages from stanc:
Warning in '/tmp/httpstan_syho537j/model_xpgz4qnv.stan', line 84, column 24: Argument
    0.05 suggests there may be parameters that are not unit scale; consider
    rescaling with a multiplier (see manual section 22.12).
Warning in '/tmp/httpstan_syho537j/model_xpgz4qnv.stan', line 54, column 12: A
    control flow statement depends on parameter(s): phi.
Warning: Your Stan program has a parameter phi with a lower and upper bound
    in its declaration. These hard constraints are not recommended, for two
    reasons: (a) Except when there are logical or physical constraints, it is
    very unusual for you to be sure that a parameter will fall inside a
    specified range, and (b) The infinite gradient induced by a hard
    constraint can cause difficulties for Stan's sampling algorithm. As a
    consequence, we recommend soft constraints rather than hard constraints;
    for example, instead of constraining an elasticity parameter to fall
    between 0, and 1, leave it unconstrained and give it a normal(0.5,0.5)
    prior distribution.
Warning: The parameter serpentines has no priors. This means either no prior
    is provided, or the prior(s) depend on data variables. In the later case,
    this may be a false positive.
Warning: The parameter oh_saponites has no priors. This means either no prior
    is provided, or the prior(s) depend on data variables. In the later case,
    this may be a false positive.
Warning: The parameter magnetite has no priors. This means either no prior is
    provided, or the prior(s) depend on data variables. In the later case,
    this may be a false positive.
Warning: The parameter hoh_oh has no priors. This means either no prior is
    provided, or the prior(s) depend on data variables. In the later case,
    this may be a false positive.
Warning: The parameter h2o_saponites has no priors. This means either no
    prior is provided, or the prior(s) depend on data variables. In the later
    case, this may be a false positive.
Warning: The parameter fe32_charge has no priors. This means either no prior
    is provided, or the prior(s) depend on data variables. In the later case,
    this may be a false positive.
Warning: The parameter fe2_crystal_2 has no priors. This means either no
    prior is provided, or the prior(s) depend on data variables. In the later
    case, this may be a false positive.
Warning: The parameter fe2_crystal_1 has no priors. This means either no
    prior is provided, or the prior(s) depend on data variables. In the later
    case, this may be a false positive.
Warning: The parameter common_feats has no priors. This means either no prior
    is provided, or the prior(s) depend on data variables. In the later case,
    this may be a false positive.


# you can def change the guess to whatever you want as long as it's within the allowed bounds of the data
# so you can't let stan do it because it just puts everything at 0 or something

initial_guess = [{'sigma':np.random.uniform(0,0.1, size = 9), 
                  'phi':np.random.uniform(0,1, size = 9), 
                  'epsilon':1, 
                  'mus':np.array(linelist['mean']), 
                  'yt':spectrum['col4']}, 
                 {'sigma':np.random.uniform(0,0.1, size = 9), 
                  'phi':np.random.uniform(0,1, size = 9), 
                  'epsilon':1, 
                  'mus':np.array(linelist['mean']), 
                  'yt':spectrum['col4']},
                {'sigma':np.random.uniform(0,0.1, size = 9), 
                  'phi':np.random.uniform(0,1, size = 9), 
                  'epsilon':1, 
                  'mus':np.array(linelist['mean']), 
                  'yt':spectrum['col4']}]


draws = fit.sample(num_chains = 3, 
                   num_samples = 1000,
                   init=initial_guess, 
                   num_warmup = 1000, delta = 0.9) # sample (3 chains of 5000 burn-in steps + 5000 sampling steps each)

# this is 1000 + 1000 steps just to make sure it runs through!
# for science runs we did 5000 + 5000 steps

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Messages received during sampling:
  Gradient evaluation took 0.012312 seconds
  1000 transitions using 10 leapfrog steps per transition would take 123.12 seconds.
  Adjust your expectations accordingly!
  Gradient evaluation took 0.012522 seconds
  1000 transitions using 10 leapfrog steps per transition would take 125.22 seconds.
  Adjust your expectations accordingly!
  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
  Exception: normal_lpdf: Location parameter[299] is -nan, but must be finite! (in '/tmp/httpstan_piuw8uz1/model_xpgz4qnv.stan', line 89, column 4 to column 24)
  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
  Exception: normal_lpdf: Location parameter[299] is -nan, but must be finite! (in '/tmp/httpstan_piuw8uz1/model_xpgz4qnv.stan', line 89, column 4 to column 24)
  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
  Gradient evaluation took 0.002603 seconds
  1000 transitions using 10 leapfrog steps per transition would take 26.03 seconds.
  Adjust your expectations accordingly!


# widths, weights, intercepts, and true values
sigma = np.median(draws['sigma'], axis = 1)
phi = np.median(draws['phi'],axis = 1)
eps = np.median(draws['epsilon'],axis = 1)
yt = np.median(draws['yt'], axis = 1)

# and all the means
common_feats  = np.median(draws["common_feats"])
fe32_charge   = np.median(draws["fe32_charge"])
fe2_crystal_1 = np.median(draws["fe2_crystal_1"])
magnetite     = np.median(draws["magnetite"])
fe2_crystal_2 = np.median(draws["fe2_crystal_2"])
serpentines   = np.median(draws["serpentines"])
oh_saponites  = np.median(draws["oh_saponites"])
h2o_saponites = np.median(draws["h2o_saponites"])
hoh_oh        = np.median(draws["hoh_oh"])

means = [common_feats,fe32_charge,
         fe2_crystal_1,magnetite,
         fe2_crystal_2,serpentines,
         oh_saponites ,h2o_saponites,
         hoh_oh]


fig, ax = plt.subplots(1, 2, figsize = (12, 5))

# plot the observed spectrum
ax[0].plot(x, spectrum['col4'], '-', color = mc[5], lw = 2, label = 'Observed spectrum')

# plot the best fit spectrum
ax[0].plot(x, yt, 'k--', lw = 2, label = 'Best-fit spectrum')

# plot the best-fit components
f = []
for i,m in zip(range(9),means):
    ax[1].plot(x, -phi[i]*fast.G(x, m, sigma[i]) + eps, 'k--', zorder = 10)
    
    # and the initial guesses
    #ax[1].plot(x, -initial_guess[0]['phi'][i]*fast.G(x, initial_guess[0]['mus'][i], 
    #                                              initial_guess[0]['sigma'][i]) + 1, 'k:', label = ['Initial guess' if i == 0 else '__None'][0])

# format
fig.legend(loc = 'upper center', bbox_to_anchor = (0.5, -0.05))
ax[0].set_xlabel(r"$\lambda$ (micron)"); ax[1].set_xlabel(r"$\lambda$ (micron)")
ax[0].set_ylabel(r"Reflectance")


plt.show()


# means

ax = az.plot_trace(draws, var_names = ['phi', 'sigma', 'common_feats',
                                       'fe32_charge',
                                       'fe2_crystal_1',
                                       'magnetite',
                                       'fe2_crystal_2',
                                       'serpentines',
                                       'oh_saponites',
                                       'h2o_saponites',
                                       'hoh_oh', 
                                      'epsilon'])



plt.tight_layout()

plt.show()


az.plot_autocorr(draws, var_names = ['phi', 'sigma', 'epsilon'] )

plt.tight_layout()
plt.show()

/home/heigerma/.local/lib/python3.8/site-packages/arviz/plots/plot_utils.py:271: UserWarning: rcParams['plot.max_subplots'] (40) is smaller than the number of variables to plot (57) in plot_autocorr, generating only 40 plots
  warnings.warn(


az.plot_ess(draws, var_names = ['phi', 'sigma', 'epsilon'])

plt.tight_layout()
plt.show()


az.plot_pair(draws, kind = 'kde', marginals = True, var_names = ['sigma'])

plt.tight_layout()
plt.show()

/home/heigerma/.local/lib/python3.8/site-packages/arviz/plots/backends/matplotlib/pairplot.py:232: UserWarning: rcParams['plot.max_subplots'] (40) is smaller than the number of resulting pair plots with these variables, generating only a 8x8 grid
  warnings.warn(


az.plot_pair(draws, kind = 'kde', marginals = True, var_names = ['phi'])

plt.tight_layout()
plt.show()


az.plot_pair(draws, kind = 'kde', marginals = True, var_names = ['common_feats',
                                       'fe32_charge',
                                       'fe2_crystal_1',
                                       'magnetite',
                                       'fe2_crystal_2',
                                       'serpentines',
                                       'oh_saponites',
                                       'h2o_saponites',
                                       'hoh_oh'])

plt.tight_layout()
plt.show()


az.plot_energy(draws)

plt.show()

Feature	label	name	left	right	mean
str76	str66	str13	float64	float64	float64
(?) common in CI spect.	Characteristic feature of Cl1	common_feats	0.45	0.5	0.475
Fe3+ - Fe2+ charge transfers	Fe3+ - Fe2+ charge transfers	fe32_charge	0.65	0.8	0.725
Fe2+ crystal field transitions in Fe2+- bearing phyllosilicates	Fe2+ crystal field transitions in Fe2+ bearing phyllosilicates (1)	fe2_crystal_1	0.9	0.95	0.925
magnetite	Magnetite	magnetite	0.98	1.03	1.005
Fe2+ crystal field transitions in Fe2+-bearing phyllosilicates	Fe2+ crystal field transitions in Fe2+ bearing phyllosilicates (2)	fe2_crystal_2	1.1	1.15	1.125
Serpentines (from OH)	Serpentines	serpentines	1.38	1.38	1.38
Saponites (from OH, sharp bands)	Saponites indicative of OH	oh_saponites	1.39	1.42	1.405
Saponites (from H2O, sharp bands)	Saponites indicative of H2O	h2o_saponites	1.42	1.5	1.46
Combination band dude to H-O-H bending plus O-H stretching\n(presence of H2O)	H-O-H bending plus O-H stretching	hoh_oh	1.9	1.92	1.91

col1	col2	col3	col4
float64	float64	float64	float64
0.4	1.0443620527697652	0.7638018711709978	1.0
0.405	1.0387604255860652	0.7528158346733661	1.0
0.41	1.0297766279058747	0.735196609765092	1.0
0.415	1.0220452396987314	0.7200336383220457	1.0
0.42	1.0128334882370613	0.7019673453599757	1.0
0.425	1.0074007359258625	0.6913125100387147	1.0
0.43	1.0003041014962957	0.6773944318987707	1.0
0.435	0.9994942571569267	0.6758061470704628	0.9985344605890577
0.44	0.995487407598298	0.6679478241139288	0.9869234293657517
0.445	0.9917628524107337	0.6606431431906622	0.976130429543084
0.45	0.9911640425318543	0.6594687438654708	0.9743952008805754
0.455	0.9848960228298765	0.64717576345896	0.9562317606507735
...	...	...	...
2.485	1.0035999550005628	0.6838583334940227	1.0
2.49	1.0042568968223469	0.6851467424855996	1.0
2.495	1.0013607561213531	0.6794667665786029	1.0
2.5	1.0005158563767573	0.6778097303056466	1.0
2.505	1.0036466814224008	0.6839499743974391	1.0
2.51	0.999890426661722	0.6765831235625068	0.9996824788569244
2.515	0.9956270617709408	0.6682217170002968	0.9873281186198138
2.52	0.9924351610742185	0.6619616899758196	0.9780786426639412
2.525	0.997633033863165	0.6721558743256062	0.9931410158237375
2.53	1.0004473272198613	0.6776753293906763	1.0
2.535	1.000395541804374	0.6775737666757844	1.0
2.54	0.9999245842150325	0.676650114119899	0.9997814604663402
2.545	1.005000402536877	0.6866049225193932	1.0

Maybe one day we'll find an asteroid that will bring life to Mars¶

Imports¶

Data¶

Load the real spectrum¶

Properties of the spectrum¶

Plot it¶

Specify the model¶

Make a dictionary of the data for stan¶

Build the model¶

Sample¶

Get estimates of the parameters¶

Results¶

Best-fit¶

Diagnostics¶

Trace plot¶

Autocorrelation time¶

Effective sample size¶

Corner plot¶

Energy plot¶